This paper traces the recent debate over the legitimacy of maturity mismatching and fractional reserve banking. It shows that there is common ground between Bagus and Howden :399–406, 2009, 106:295–300, 2012) on the one hand and Evans on the other regarding contractual arrangements that lead to fractional reserve banking, while both agree that fractional reserve banking that arises out of a bailment or storage contract constitutes fraud. Block and Barnett :711–716, 2009, 100:229–238, 2011) stress the illegitimacy of (...) fractional reserve banking for creating more money substitutes than there is actual money. While it is true that fractional reserve banks are capable of creating money, this activity still cannot be regarded as fraudulent using a common law definition of fraud for it can only take place with requisite client collaboration that makes it impossible to identify a victim. (shrink)

In this article we reply to George Selgin’s counterarguments to our article “Fractional Reserve Free Banking: Some Quibbles”. Selgin regards holding cash as saving while we focus on the real savings necessary to maintain investment projects. Real savings are unconsumed real income. Variations in real savings are not [...].

The necessity for a government “lender of last resort” has been advanced as a justification for central banking. In this paper, I compare lending practices under central banking with those that would be likely to exist under a system of fractional-reserve free banking (FRFB). To do this I examine the underlying nature of banks as warehousing and credit-granting institutions and consider how redemption runs can arise as a consequence of fractional reserves in this system. Following the work (...) of Thornton and Bagehot, I describe principles of prudent lending that can be used to stem a redemption run when it arises. I examine the market incentives that apply under FRFB and how these incentives are perverted under a system of central banking. I find that a government central bank is not well-placed to lend according to prudent standards, and in fact is likely to use its power to pursue political goals that are at odds with prudent lending. I examine the US financial crisis and the actions of the Federal Reserve System to illustrate this view. (shrink)

In a number of recent articles, the debate on the ethics of fractional reserve “free” banking has been extended to loan maturity mismatching, specifically the banking practice of borrowing short and lending long. Barnett and Block :711–716, 2009; 2010) claim the practice is illicit, because like fractional reserve banking it creates duplicate property titles. They argue there is a continuum in the time dimension between the two kinds of activities. Bagus and Howden :399–406, 2009; 106:295–300, 2012a; Eur J (...) Law Econ, 2012b; Bus Ethics 22:235–245, 2013) maintain that loan maturity mismatching does not create duplicate titles and is not illicit, and that from an economic and legal perspective there is no continuum with fractional reserve banking. Cachanosky and Evans enter the debate from the free-banking standpoint and view both practices as legitimate. In this paper, I agree with the conclusions of Bagus and Howden, but adopt a different approach to support this position. Using the title-transfer theory of contract, I demonstrate from first principles why loan maturity mismatching does not create duplicate property titles and is a legitimate practice. Employing this same theory, I then present a novel argument to show why the contractual arrangements found in fractional reserve banking are logically contradictory and illegitimate. (shrink)

In this article we consider an argument put forth by Selgin in support of the claim that there exists a mechanism for limiting coordinated expansions of fiduciary media under a system of fractional reserve free banking. Selgin argues that such banks hold risk-adjusted reserves against expected losses, and even if the expectation of reserve losses remains zero, the variance of such losses increases under an in-concert expansion . It is this increased variability that is claimed to act as (...) a brake on the expansion. We take issue with this argument on the basis of the fact that such a characterization of observed clearings would require that characteristics of the underlying data-generating process be obtainable from pathwise realizations of that process. In other words, there is an implicit assumption of stationarity in Selgin’s argument, and this assumption is at odds with well-known empirical facts of non-stationarity associated with most economic time series. We also point out ways in which techniques of risk management commonly found in the modern financial industry are unlikely to be effective in addressing this problem. (shrink)

In Time Deposits, Dimension, and Fraud (2009), William Barnett and Walter Block argue that by borrowing short and lending long there is an over issuance of property rights. Their article, however, does not fully extend the consequences of their contribution. Once this is done, it becomes clearer that their argument suits a great impediment to banking, becoming a possible reason to support rather than to oppose fractional reserve banking. Bagus and Howden (J Bus Ethics 90(3):399–406, 2009) comment on Barnett (...) and Block (J Bus Ethics 88(4):711–716, 2009), the authors claim that while maintaining the illegitimacy of fractional reserve deposits, borrowing short and lending long it is actually not illegitimate. An extension on Bagus and Howden (2009) will show that their line of argumentation can be applied as a defense of fractional reserve banking as well. (shrink)

Salerno asserts that in the debate between those who favor and oppose fractional reserve banking, the important issue is not whether or not this institution is inherently fraudulent, but, rather, does it or does it not cause the business cycle. We join this author in thinking both important; however, we reverse this order.

This article contributes to a recent debate between Barnett and Block : 711–716, 2009), Bagus and Howden : 399–406, 2009), Barnett and Block, Cachanosky and Bagus and Howden regarding the conceptual distinction between demand deposits and time deposits. It is argued that from an economic perspective there is nothing inherently fraudulent or illegitimate about deposit accounts that are available ‘on demand’, but that this relies on certain contractual provisions. Particular attention is drawn to option clauses and withdrawal clauses, which “solve” (...) the problems raised by Barnett and Block, and Bagus and Howden. Previous authors have also neglected the asset side of banks balance sheets, and this is shown to further justify the legitimacy of fractional reserve banking. (shrink)

Barnett and Block (Journal of Business Ethics, 2009 ) attack the heart of modern banking by claiming that the practice of borrowing short and lending long is illicit. While their claim of illegitimacy concerning fractional reserve banking can be defended, their justification lacks substance. Their claim is herein strengthened by a legal analysis of deposits and loans based on Huerta de Soto (Money, Bank Credit and Economic Cycles, 2006 ). A combined legal and economic analysis shows that while lending (...) deposits can be regarded as illicit, the maturity mismatching of loans is legitimate contrary to Barnett and Block’s claim. No over-issuance of property rights is involved with this practice once the distinction between present and future goods is taken into account. However, while the practice is not illicit per se , it is greatly assisted and developed through the presence of a fractional reserve banking system, and can sometimes breed detrimental effects. (shrink)

Barnett and Block (J Bus Ethics 18(2):179–194, 2011 ) argue that one cannot distinguish between deposits and loans due to the continuum problem of maturities and because future goods do not exist—both essential characteristics that distinguish deposit from loan contracts. In a similar way but leading to opposite conclusions (Cachanosky, forthcoming) maintains that both maturity mismatching and fractional reserve banking are ethically justified as these contracts are equivalent. We argue herein that the economic and legal differences between genuine deposit (...) and loan contracts are clear. This implies different legal obligations for these contracts, a necessary step in assessing the ethics of both fractional reserve banking and maturity mismatching. While the former is economically, legally, and perhaps most importantly ethically problematic, there are no such troubles with the latter. (shrink)

If fractional-reserve demand deposits are common, and illegitimate, an obvious flaw in the banking system is exposed. However, this article maintains that the only reason why demand deposits may be considered illegitimate is because of a way of defining them that renders them almost irrelevant. This article provides a response to Bagus et al., and identifies examples of how they misrepresent Evans. It also provides further considerations on the tradeoffs relating to the availability of a deposit; methodological subjectivism; and (...) the potential for hybrid contracts. Deposit and loan contracts may be hard to mix, but the actual results of doing so should not be ignored. (shrink)

We stipulate, arguendo, that fractional-reserve-demand deposit banking is per se fraudulent. We ask whether or not time deposit banking can also be illicit, and answer in the positive, if there is a mismatch between the time dimensions of deposits and loans. To wit, if an intermediary borrows short and lends long.

We stipulate, arguendo, that fractional-reserve-demand deposit banking is per se fraudulent. We ask whether or not time deposit banking can also be illicit, and answer in the positive, if there is a mismatch between the time dimensions of deposits and loans. To wit, if an intermediary borrows short and lends long.

The necessity for a government “lender of last resort” has been advanced as a justification for central banking. In this paper, I compare lending practices under central banking with those that would be likely to exist under a system of fractional-reserve free banking (FRFB). To do this I examine the underlying […].

This paper investigates ontological dimensions of the blockchain by asking what kind of socio-technical object bitcoin is. It discusses both blockchain's political qualities and the political forms enabled by its emergence. It first observes recent approaches to the ontology of money and the political qualities of the ledgers used by the current fractional reserve banking model. It then directs the same questions at blockchain technology. The paper discusses an ontology proposed by Ole Bjerg and argues in favour of a (...) mixed-ontology approach to blockchains. It then questions the political qualities of the distributed ledger as a digital object and highlights the apparent absence of authority figures in the model. Finally, it argues that the political ontology of the blockchain can be framed as the displacement of authority from institutional actors into instrumental control of trust, in a dynamically distributed environment. (shrink)

How ethical have recent banking practices been? We answer this question via an economic analysis. We assess the two dominant practices of the modern banking system – fractional reserves and maturity transformation – by gauging the respective rights of the relevant parties. By distinguishing the legal and economic differences between deposit and loan contracts, we determine that the practice of maturity transformation (in its various guises) is not only ethical but also serves a positive social function. The foundation (...) of the modern banking system – the holding of fractional reserves against deposits – is, however, problematic from economic, legal and ethical perspectives. Starting from a microanalysis of money's function, a reassessment of the current laws concerning the practice is encouraged, with the aim not only to rectify economic irregularities but also to realign depositors' rights with the obligations of the banking sector. (shrink)

How ethical have recent banking practices been? We answer this question via an economic analysis. We assess the two dominant practices of the modern banking system – fractional reserves and maturity transformation – by gauging the respective rights of the relevant parties. By distinguishing the legal and economic differences between deposit and loan contracts, we determine that the practice of maturity transformation (in its various guises) is not only ethical but also serves a positive social function. The foundation (...) of the modern banking system – the holding of fractional reserves against deposits – is, however, problematic from economic, legal and ethical perspectives. Starting from a microanalysis of money's function, a reassessment of the current laws concerning the practice is encouraged, with the aim not only to rectify economic irregularities but also to realign depositors' rights with the obligations of the banking sector. (shrink)

In the present paper we argue that the theory of contracts embraced by many libertarian scholars and relied upon by them in sundry important debates (e.g. over morality of the fractional reserve banking or loan maturity mismatching etc.), that is, the title transfer theory of contracts (TTT) should be rejected as not being able to account for the binding force of future-oriented contracts, including contracts deemed enforceable by those scholars themselves. The TTT claims that the only contracts that should (...) be legally binding are these where the debtor’s failure to abide by them constitutes a violation of the creditor’s private property rights. However, as we argue, no default of the debtor in a future-oriented contract can in itself amount to such a violation. (shrink)

In this paper we extend an argument originally developed in Hülsmann to analyze changes to the structure of production that occur when the demand for money changes. In particular, we show that Hülsmann’s argument, which contrasted such changes under commodity and fiat systems, applies as well to the case of 100% reserve systems contrasted with fractional reserve free banking systems . Specifically, we argue that under a 100% reserve system, the structure of production will change in response to a (...) change in demand for money, and that it will not under FR/FB. In fact, such changes are beneficial. Since one of the central arguments in defense of FR/FB is precisely the fact that it avoids such changes to the structure of production , we conclude that this argument amounts to comparing different mechanisms for attaining different equilibrium states, and hence is invalid as a defense of that mechanism as such. (shrink)

Depositors have perceived banks as acting unethically during the most recent recession. One area of consternation is the ambiguity of the legal obligations entailed by the deposit contract when it is backed with only fractional reserves. In this article, we apply an existing analysis of the legitimacy and ethicality of banking practices to a wider range of financial transactions, including insurance policies, securities lending, perpetual bonds, and callable loans. Securities lending in particular creates rights violations analogous to those (...) in fractional-reserve banking. Both callable loans and perpetual bonds have clear legal obligations which are not inherently problematic, though we herein clarify what these obligations are. Finally, we apply our ethical framework to demonstrate that insurance products are distinct from banking deposit contracts, and that perceived parallels between the two products underestimate these differences. (shrink)

The conventional view of banking crises sees them as an inherent problem of fractional?reserve banking systems. According to this view, government regulation in the form of an alert central bank (acting as a ?lender of last resort"), or deposit insurance, or both is needed to keep isolated bank failures from generating systemwide panic. But this view does not mesh with historical experience, which points to government regulation itself as the most likely cause of banking crises.

Barnett and Block establish that not only are fractional reserve demand deposits fraudulent and create an Austrian Business Cycle , but that a certain type of mismatching between time deposits and the period for which the depository institution relends the deposited funds are also contrary to libertarian law. The question we address in the present paper is whether or not this type of disconnect between the period for which the ultimate lender committed funds and the ultimate borrower gained possession (...) thereof also necessarily start an Austrian Business Cycle. Even though this does not constitute an increase in the stock of money, we answer in the affirmative. (shrink)

The pioneering sociologist William Graham Sumner was a prolific and astute historian of the early American republic, whose work was informed by his classical liberalism and his understanding of economics. He authored seven major works including biographies and thematic studies concentrating on the vital subjects of currency, banking, business cycles, foreign trade, protectionism, and politics. Although his works are out of print, and hardly mentioned or referred to by historians or economists, they are quite valuable for understanding the politics and (...) major economic issues of the first century of the republic.1 They are: History of American Currency, Lectures on the History of Protection, Andrew Jackson, Alexander Hamilton, The Financier and Finances of the American Revolution, 2 vols., Robert Morris, History of Banking in the United States. As one can see, Sumner was most interested in the history of money and banking in America. He was a resolute opponent of inflation, inconvertible currencies, legal tender laws, bimetallic standards, and the American practice of fractional-reserve banking. His theory of the business cycle was built on the work of antebellum political economists such as Condy Raguet. Sumner’s understanding of it is sophisticated and proto- Austrian. (shrink)

Cette réaction est suscitée par l’article de Laurent Le Maux, récemment publié dans ce Journal. Le Maux affirme que Ludwig von Mises était le défenseur d’un système de réserves fractionnaires et un précurseur des économistes contemporains partisans des réserves fractionnaires. Nous critiquons la manière dont Le Maux utilise la littérature ancienne dans ce domaine, et nous montrons qu’il n’est pas suffisamment au fait des travaux de Mises et des problèmes qui divisent les défenseurs et les opposants du système de réserves (...) fractionnaires. Les écrits de Ludwig von Mises fournissent la preuve accablante qu’il était, et il le disait lui-même, un économiste qui développait l’approche de la Currency School dans le domaine des problèmes bancaires.This paper takes issue with an article by Laurent Le Maux that recently appeared in this journal. Le Maux claims that Ludwig von Mises was an advocate of fractional-reserve banking and a precursor of presentday economists defending fractional reserves. We criticise Le Maux’s treatment of previous literature in the field, and show that he is insufficiently acquainted with Mises’ work and with the problems that divide advocates and opponents of fractional reserves. Ludwig von Mises’ writings provide overwhelming evidence that he was, and saw himself as, an economist who developed the approach of the Currency School toward problems of banking. (shrink)

Cette réaction est suscitée par l’article de Laurent Le Maux, récemment publié dans ce Journal. Le Maux affirme que Ludwig von Mises était le défenseur d’un système de réserves fractionnaires et un précurseur des économistes contemporains partisans des réserves fractionnaires. Nous critiquons la manière dont Le Maux utilise la littérature ancienne dans ce domaine, et nous montrons qu’il n’est pas suffisamment au fait des travaux de Mises et des problèmes qui divisent les défenseurs et les opposants du système de réserves (...) fractionnaires. Les écrits de Ludwig von Mises fournissent la preuve accablante qu’il était, et il le disait lui-même, un économiste qui développait l’approche de la Currency School dans le domaine des problèmes bancaires.This paper takes issue with an article by Laurent Le Maux that recently appeared in this journal. Le Maux claims that Ludwig von Mises was an advocate of fractional-reserve banking and a precursor of presentday economists defending fractional reserves. We criticise Le Maux’s treatment of previous literature in the field, and show that he is insufficiently acquainted with Mises’ work and with the problems that divide advocates and opponents of fractional reserves. Ludwig von Mises’ writings provide overwhelming evidence that he was, and saw himself as, an economist who developed the approach of the Currency School toward problems of banking. (shrink)

In the pages of this journal, a fruitful debate has evolved on the ethical legitimacy of fractional-reserve banking. In this article, we respond to the new arguments raised by Evans as we clarify our position on the unethical and illegitimate nature of fractional-reserve banking. Fractional-reserve banking is not a recent financial innovation but represents a long-standing legal aberration. The co-mingling of two mutually exclusive financial contracts, deposit and loan, confounds the contracting parties’ purposes, intents, rights, and obligations. (...) As a result, it creates unsolvable legal difficulties and ethical dilemmas. While these problems are most evident in the case of a bank run, they also arise when trying to answer the simple question of “who owns a deposit?”. (shrink)

Barnett and Block claim that Bagus and Howden support indirectly the concept of market failure. In this paper, we show that maturity mismatching in an unhampered market may imply entrepreneurial error but cannot be considered a market failure. We demonstrate why fractional-reserve banking leads to business cycles even if there is no central bank and why maturity mismatching does not per se lead to clusters of errors in a free market. Finally, in contrast to the examples provided by Barnett (...) and Block, we assure that maturity mismatching does not imply the creation of two incompatible contracts due to the fungible nature of money. (shrink)

What role do demand deposits serve in the financial system? The answer to this simple question has great implications in keeping the legal terms of the contract consistent with the demands of the financial system. Demand deposits are a perfect monetary substitute. Since money is only held to hedge against perceived uncertainty in both the timing and magnitude of future expenditures, demand deposits are demanded for the same reason. From this we derive three main conclusions. First, a financial contract similar (...) to a demand deposit cannot substitute for money. Second, full agreement to a financial contract does not create a perfect substitute for money unless it provides money’s two key characteristics: on demand and par value redemption. Finally, the demand for fractional-reserve demand deposits is fostered by an exogenous source and that demand for a good or service is not a sufficient condition to justify its legality or ethicality. (shrink)

In Barnett and Block (J Bus Ethics 88(4):711–716, 2009a), the present authors claim that borrowing short and lending long is fraudulent, and thus ought to be prohibited on legal grounds. Bagus and Howden (J Bus Ethics 90(3):399, 2009) take issue with our ethical analysis. The present paper is our response to these authors; it is an attempt to defend Barnett and Block (J Bus Ethics 88(4):711–716, 2009a) against the very interesting and important, although we believe, erroneous, criticisms of Bagus and (...) Howden (J Bus Ethics 90(3):399, 2009). (shrink)

We address the most fundamental yet routinely ignored issue in economics today: that of distributive impact of the monetary system on the real economy. By re-examining the logical implications of token re-presentation of value and Irving Fisher’s theory of exchange, we argue that producers of value incur incidental expropriation of wealth associated with the deflationary effect that new value supply has on the purchasing power of money. In order to remedy the alleged inequity we propose a value-added negative tax (VANT) (...) based on net individual contribution to the economic output, which is structured as a negative tax function geared to profits derived from eligible productive activities in consideration of their estimated deflationary impact. We show that an adequately optimised VANT can be non-inflationary and have zero net cost to the public. Furthermore, economic output stands to improve due to direct incentivisation of value creation, making the proposed scheme not only politically feasible but economically desirable. The proposal advances the principle of ‘fair money’, where all forms of economic value are attributed to their rightful owners prior to any positive taxation. (shrink)

In a spirit of collegial support, this paper argues that Beckett and Hager’s theoretical justification and empirical exemplifications do not do full justice to the complexity of group or team learning. We firstly reaffirm our support for the theoretical argument Becket and Hager make, though expressing some reservations about Complexity Theory, to explain the taken-for-granted assumptions that learning by an individual is the paradigm case of learning and that context plays a minimal role in this process. Drawing on our joint (...) and separate work, we demonstrate that Becket and Hager’s argument is less radical than it may initially seem because it is predicated on: (i) cognitive-bounded rather than “distributed” or “extended” conception of mind; (ii) material rather than a “immaterial” conception of activity; and (iii) co-present rather than a “fractional” or “connective” conception of ontology. Despite making this critique, we conclude by making the case that we are adding further substance to Becket and Hager’s overarching argument and, in doing so, encouraging them to be more radical about how they conceptualise the complexity of learning. (shrink)

Reproduction places severe demands on the energy metabolism in human females. When physical work entails higher energy expenditure, not enough energy will be left for the support of the reproductive processes and temporal suppression of the reproductive function is expected. While energy needed for reproduction may be obtained by increases in energy intake, utilization of fat reserves, or reallocation of energy from basal metabolism, several environmental or physiological constraints render such solutions unlikely. For human ancestors increases in energy intake (...) were limited by availability of food, by labor of food preparation and by metabolic ceilings to energy assimilation. Energy stored as fat may support only a fraction of the requirements for reproduction (especially lactation). Effects of intense physical activity on basal metabolism may also interfere with fat accumulation during pregnancy. Finally, the female physiology may experience demands on increasing the basal metabolism as a consequence of physical activity and, at the same time, on decreasing the basal metabolism, when energy to support the ongoing pregnancy or lactation is inadequate. The resulting metabolic dilemmas could constitute a plausible cause for the occurrence of reproductive suppression in response to physical activity. It is, therefore, likely that allocating enough energy to the reproductive processes during periods when energy expenditure rises may be difficult due to physiological and bioenergetic constraints. Females attempting pregnancy in such conditions may compromise their lifetime reproductive output. A reproductive suppression occurring in low energy availability situations may thus represent an adaptive rather then a pathological response. (shrink)

Rare copy number variants have a prominent role in the aetiology of schizophrenia and other neuropsychiatric disorders. Substantial risk for schizophrenia is conferred by large CNVs at several loci, including microdeletions at 1q21.1, 3q29, 15q13.3 and 22q11.2 and microduplication at 16p11.2. However, these CNVs collectively account for a small fraction of cases, and the relevant genes and neurobiological mechanisms are not well understood. Here we performed a large two-stage genome-wide scan of rare CNVs and report the significant association of copy (...) number gains at chromosome 7q36.3 with schizophrenia. Microduplications with variable breakpoints occurred within a 362-kilobase region and were detected in 29 of 8,290 patients versus 2 of 7,431 controls in the combined sample. All duplications overlapped or were located within 89 kilobases upstream of the vasoactive intestinal peptide receptor gene VIPR2. VIPR2 transcription and cyclic-AMP signalling were significantly increased in cultured lymphocytes from patients with microduplications of 7q36.3. These findings implicate altered vasoactive intestinal peptide signalling in the pathogenesis of schizophrenia and indicate the VPAC2 receptor as a potential target for the development of new antipsychotic drugs. © 2011 Macmillan Publishers Limited. All rights reserved. (shrink)

_341_ _Objectives: _In patients with multivessel disease both the detection of the culprit lesion and the exact allocation are important preconditions for sufficient treatment and improved outcome. In a vessel based approach the combination of quantitative coronary angiography and fractional flow reserve measured by a pressure wire should be advantageous compared to myocardial SPECT, as morphological and functional information is delivered simultaneously. Therefore our aim was to evaluate MS in the detection and allocation of hemodynamically significant stenoses obtained by (...) the combined gold standard QCA plus FFR in patients with multivessel disease. _Methods: _FFR and QCA of 95 vessels in 80 patients have been evaluated. Hemodynamically significant target lesions were defined as intermediate stenoses between 50 and 75% with an FFR. (shrink)

Edward Titchener, one of the great champions of introspectionist psychology, declared that 'the term Introspection, as we find it used today, is highly equivocal, and that the procedure which it connotes may be scientifically illegitimate, or even wholly imaginary' . He made the point because he wanted to insulate his preferred method of doing psychological research from criticisms that were directed against forms of introspection that he conceded to be unreliable. The point, however, is not just that we can introspect (...) more or less carefully. It is that there are 'gross differences in the meaning of the word' . 'Introspection' is Janus-faced. It splinters into several different species, involving different underlying mechanisms. (shrink)

This paper is dedicated to extending and adapting to modal logic the approach of fractional semantics to classical logic. This is a multi-valued semantics governed by pure proof-theoretic considerations, whose truth-values are the rational numbers in the closed interval $[0,1]$. Focusing on the modal logic K, the proposed methodology relies on three key components: bilateral sequent calculus, invertibility of the logical rules, and stability (proof-invariance). We show that our semantic analysis of K affords an informational refinement with respect to (...) the standard Kripkean semantics (a new proof of Dugundji’s theorem is a case in point) and it raises the prospect of a proof-theoretic semantics for modal logic. (shrink)

Although many researchers theorize that primitive numerosity processing abilities may lay the foundation for whole number concepts, other classes of numbers, like fractions, are sometimes assumed to be inaccessible to primitive architectures. This research presents evidence that the automatic processing of nonsymbolic magnitudes affects processing of symbolic fractions. Participants completed modified Stroop tasks in which they selected the larger of two symbolic fractions while the ratios of the fonts in which the fractions were printed and the overall sizes of the (...) compared fractions were manipulated as irrelevant dimensions. Participants were slower and less accurate when nonsymbolic dimensions of printed fractions were incongruent with the symbolic comparison decision. Results indicated a robust basic sensitivity to nonsymbolic ratios that exceeds prior conceptions about the accessibility of fraction values. Results also indicated a congruity effect for overall fraction size, contrary to findings of prior research. These findings have implications for extending theory about the nature of human number sense and mathematical cognition more generally. (shrink)

Consider syllogisms in which fraction (percentage) quantifiers are permitted in addition to universal and particular quantificrs, and then include further quantifiers which are modifications of such fractions (such as "almost ½ the S are P" and "Much more than ½ the S are P"). Could a syllogistic system containing such additional categorical forms be coherent? Thompson's attempt (1986) to give rules for determining validity of such syllogisms has failed; cf. Carnes & Peterson (forthcoming) for proofs of the unsoundness and incompleteness (...) of Thompson's rules. Building on Peterson (1985), the coherence of such a syllogistic can, however, be demonstrated with an algebra which provides its semantics; e.g., "almost ¾ the S arc P'" is represented as " -(3(SP) » SP)". (shrink)

In the paper we construct a new kind of fractional dynamical model, i.e. the fractional relativistic Yamaleev oscillator model, and explore its dynamical behaviors. We will find that the fractional relativistic Yamaleev oscillator model possesses Lie algebraic structure and satisfies generalized Poisson conservation law. We will also give the Poisson conserved quantities of the model. Further, the relation between conserved quantities and integral invariants of the model is studied and it is proved that, by using the Poisson (...) conserved quantities, we can construct integral invariants of the model. Finally, the stability of the manifold of equilibrium states of the fractional relativistic Yamaleev oscillator model is studied. The paper provides a general method, i.e. fractional generalized Hamiltonian method, for constructing a family of fractional dynamical models of an actual dynamical system. (shrink)

This article presents a new semantics for classical propositional logic. We begin by maximally extending the space of sequent proofs so as to admit proofs for any logical formula; then, we extract the new semantics by focusing on the axiomatic structure of proofs. In particular, the interpretation of a formula is given by the ratio between the number of identity axioms out of the total number of axioms occurring in any of its proofs. The outcome is an informational refinement of (...) traditional Boolean semantics, obtained by breaking the symmetry between tautologies and contradictions. (shrink)

This paper introduces a possible alternative model of gravity based on the theory of fractional-dimension spaces and its applications to Newtonian gravity. In particular, Gauss’s law for gravity as well as other fundamental classical laws are extended to a D-dimensional metric space, where D can be a non-integer dimension. We show a possible connection between this Newtonian Fractional-Dimension Gravity (NFDG) and Modified Newtonian Dynamics (MOND), a leading alternative gravity model which accounts for the observed properties of galaxies and (...) other astrophysical structures without requiring the dark matter hypothesis. The MOND acceleration constant $${a_{0}} \simeq 1.2 \times 10^{-10} \text {m}\, \text{s}^{-2}$$ can be related to a natural scale length $$l_{0}$$ in NFDG, i.e., $$a_{0} \approx GM/l_{0}^{2}$$, for astrophysical structures of mass M, and the deep-MOND regime is present in regions of space where the dimension is reduced to $$D \approx 2$$. For several fundamental spherically-symmetric structures, we compare MOND results, such as the empirical Radial Acceleration Relation (RAR), circular speed plots, and logarithmic plots of the observed radial acceleration $$g_{obs}$$ vs. the baryonic radial acceleration $$g_{bar}$$, with NFDG results. We show that our model is capable of reproducing these results using a variable local dimension $$D\left( w\right)$$, where $$w =r/l_{0}$$ is a dimensionless radial coordinate. At the moment, we are unable to derive explicitly this dimension function $$D\left( w\right)$$ from first principles, but it can be obtained empirically in each case from the general RAR. Additional work on the subject, including studies of axially-symmetric structures, detailed galactic rotation curves fitting, and a possible relativistic extension, will be needed to establish NFDG as a viable alternative model of gravity. (shrink)

Reserve systems are a tool to allocate scarce resources when stakeholders do not have a single objective. This paper introduces some basic concepts about reserve systems for pandemic medical resource allocation. At the onset of the Covid-19 pandemic, we proposed that reserve systems can help practitioners arrive at compromises between competing stakeholders. More than a dozen states and local jurisdictions adopted reserve systems in initial phases of vaccine distribution. We highlight several design issues arising in some of these implementations. We (...) also offer suggestions about ways practitioners can take advantage of the flexibility offered by reserve systems. (shrink)

This paper presents a novel fractional-order PID controller tuning strategy based on Bode’s optimal loop shaping which is commonly used for LTI feedback systems. Firstly, the controller parameters are achieved based on flat phase property and Bode’s optimal reference model, so that the controlled system is robust to gain variations and can achieve desirable transient performance according to various control requirements. Then, robustness analysis of the controlled system is carried out to support the results. Furthermore, the parameter setting is (...) analyzed to demonstrate the superiority of the proposed controller. At last, some simulation examples are shown to verify the accuracy and usefulness of the proposed control strategy. The proposed fractional-order PID controller does not have any restriction on the controlled plant, so it can be widely applied on both integer-order and fractional-order systems. (shrink)